Building a Framework of Rough Inclusion Functions by Means of Computerized Proof Assistant

Grabowski, Adam

doi:10.1007/978-3-030-22815-6_18

Rough Sets

2019

DOI: 10.1007/978-3-030-22815-6_18

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Building a Framework of Rough Inclusion Functions by Means of Computerized Proof Assistant

Adam Grabowski

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Cited by 2 publications

References 26 publications

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Formal Development of Rough Inclusion Functions

Grabowski

2019

Formalized Mathematics

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Summary Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard one, κ£, connected with Łukasiewicz [14], and extend this research for two additional RIFs: κ1, and κ2, following a paper by Gomolińska [4], [3]. We also define q-RIFs and weak q-RIFs [2]. The paper establishes a formal counterpart of [7] and makes a preliminary step towards rough mereology [16], [17] in Mizar [13].

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Formal Development of Rough Inclusion Functions

Grabowski

2019

Formalized Mathematics

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Developing Complementary Rough Inclusion Functions

Grabowski

2020

Formalized Mathematics

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SummaryWe continue the formal development of rough inclusion functions (RIFs), continuing the research on the formalization of rough sets [15] – a well-known tool of modelling of incomplete or partially unknown information. In this article we give the formal characterization of complementary RIFs, following a paper by Gomolińska [4]. We expand this framework introducing Jaccard index, Steinhaus generate metric, and Marczewski-Steinhaus metric space [1]. This is the continuation of [9]; additionally we implement also parts of [2], [3], and the details of this work can be found in [7].

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Building a Framework of Rough Inclusion Functions by Means of Computerized Proof Assistant

Cited by 2 publications

References 26 publications

Formal Development of Rough Inclusion Functions

Formal Development of Rough Inclusion Functions

Developing Complementary Rough Inclusion Functions

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